Thomas Michael Nutt, 46, pleaded guilty to manslaughter at Bradford Crown Court today.
As he denies a charge of murdering Dawn Walker in October 2021, he will still stand trial in July.
The body of grandmother Ms Walker, 52, was found dumped in a suitcase on playing fields near their home in Lightcliffe.
The couple are believed to have married shortly before her death.
The brief hearing was told that the trial will rely on neuropathological evidence regarding strangulation and other injuries.
Mr Nutt has been deemed mentally fit to stand trial following a psychiatric assessment.
However he has suffered a burst hernia in prison and his defence counsel warned that as he is being treated with morphine, his ability to concentrate for long periods of time during a hearing may be affected if he is unable to have surgery before the trial.
Ms Walker's family described her as a 'loving daughter, mother, nanna, sister, auntie and friend.'